Hummingbird Ponder

Imagine for a moment that you're a hummingbird living near our home. Every day, you feed at the feeders that somehow never run out of nectar. How do you perceive those feeders and the humans that replenish them?

I got to pondering this question as I refilled our feeders this morning (five quarts of hummer juice!). I know the hummingbirds recognize me, as their behavior is much different (unafraid) with me than with other people. I can also see that they know to check out the refilled feeders when I bring them out, after leaving the empty feeders alone. So there is some consciousness there of the situation. But I wonder exactly what it is?

For instance, do the hummers see the feeders as some sort of “magic flower” that somehow never runs out of nectar? Or do they realize that the feeders are contrivances for their benefit? And how do they perceive me? As some sort of “nectar god”? If mother hummers can talk to their babies, what do they tell them about the feeders and me?

Inquiring minds want to know!

Climate Data Problem?

As if the problems with models and mis-placed incentives weren't enough, now there's good reason to be skeptical of the historical climate data that underlies the actual observations of global warming! Some skeptical climate scientists are calling into question the way in which the temperature data is being collected.

Here's the problem in a nutshell: it appears that some number of the weather stations used to collect temperature data are located improperly, in spots where the temperature is artificially high because of asphalt, reflections from buildings, or even hot equipment. The photo above shows the Wickenburg, Arizona measurement site. The temperature measuring instrument is in the white finned coffee-can shaped container sitting atop a pole – on an asphalt parking lot, next to buildings, and right next to hot equipment!

Certainly not all stations are located badly like this. Of particular interest of the stations that started out in perfectly ok locations, but which had cities and big towns grow around them, and perhaps had site “improvements” made which would introduce temperature bias. One skeptical climate scientist decided to enlist citizen help to reach the goal of surveying all of the 1,200+ stations – check out his web site here if you'd like to help. The results so far (160 sites surveyed) show a definite and substantial problem: many sites are located such that you'd expect to see temperature increases from local effects. These are the measurements being used to predict global warming, but what they're really doing is telling us that the asphalt is hot. Doh!

One of my favorite bloggers surveyed two sites, including the one in the photo above. Check out his report.

It's still true: the more I learn about global warming, especially anthropogenic global warming, the more skeptical I become...

A Ponder...

Driving in my truck yesterday, I happened to notice the odometer was getting close to 150,000 miles. My 1996 Toyota T100 has given me nearly flawless service since I bought it more than 10 years ago. Just recently I had the first expensive maintenance in its entire lifetime, and I expect that to be the last for at least another 50,000 or so miles.

But I got to pondering another significance of that 150,000 miles. All but a very few miles of that were driven by me – so that 150,000 miles represents a whole bunch of my personal time. If you figure I averaged 50 MPH over they entire life of the truck (that's optimistic), that means I have spent something like 3,000 hours driving my truck. And that doesn't even count the time I spent driving our other vehicle!

Three thousand hours on the road. I know where most of this came from: until five years ago, I had a job that required me to commute to the office every day. Until two years ago, I traveled to the office once a week. The past two years I've worked from my home, with no commute at all.

Back in the bad old days when I was a manager, we used to figure that a normal employee worked 2,000 hours per year (50 weeks at 40 hours per week). So that 3,000 hours is equivalent to a year and a half of employment. If you figure in the fact that the vast majority of my commute time in this truck happened over just six years of employment (when I was commuting every day), a year and a half of wasted time starts to be significant.

The bottom line is that both I and my employer are gaining from the absence of my commute. I'm a salaried employee and don't formally keep track of my hours – but I guarantee you they exceed 40 hours per week (ask my wife!). I gain personally as well – no more frustrating rush hour commutes, and some more free time to spend with my family, on my hobbies, or on my honey-do list (I'll let you guess where the priorities are <smile>).

I love it that my Toyota shrugs off the 150,000 miles … but I hate it that I had to waste all that time driving to find that out!

Firearms Refresher Course

From Jim M., who starts out with this quote from Thomas Jefferson:

"Those who hammer their guns into plows will plow for those who do not."

And then starts the actual course:

FIREARMS REFRESHER COURSE

1. An armed man is a citizen. An unarmed man is a subject.
   
   
2. A gun in the hand is better than a cop on the phone.
   
   
3. Colt: The original point and click interface.
   
   
4. Gun control is not about guns; it's about control.
   
   
5. If guns are outlawed, can we use swords? (Ed.: See what's happening in England, where there's a serious move afoot to outlaw knives!)
   
   
6. If guns cause crime, then pencils cause misspelled words.
   
   
7. "Free" men do not ask permission to bear arms.
   
   
8. If you don't know your rights you don't have any.
   
   
9. Those who trade liberty for security have neither.
   
   
10. The United States Constitution (c) 1791. All Rights reserved.
    
    
11. What part of "shall not be infringed" do you not understand?
    
    
12. The Second Amendment is in place in case the politicians ignore the others.
    
    
13. 64,999,987 firearms owners killed no one yesterday.
    
    
14. Guns only have two enemies; rust and politicians.
    
    
15. Know guns, know peace, know safety. No guns, no peace, no safety.
    
    
16. You don't shoot to kill; you shoot to stay alive.
    
    
17. 911 - government sponsored Dial-a-Prayer.
    
    
18. Assault is a behavior, not a device.
    
    
19. Criminals love gun control -- it makes their jobs safer.
    
    
20. If guns cause crime, then matches cause arson.
    
    
21. Only a government that is afraid of its citizens tries to control them.
    
    
22. You only have the rights you are willing to fight for.
    
    
23. Enforce the "gun control laws" we ALREADY have, don't make more.
    
    
24. When you remove the people's right to bear arms, you create slaves.
    
    
25. The American Revolution would never have happened with gun control.
    
    
26. "A government of the people, by the people, for the people..."

My guns are handy, ready to punch large holes in varmints (we have lots of those!) and bad guys…

New Poll

There's a new poll up, at the right. This one tests your understanding of the mechanics of a ship… Get it right and you might have a career in naval architecture!

Why is the Sky Blue?

I have smart readers! 60% of you who responded to the poll got the right answer: scattering. And nobody took the dunce's answer (pigment).

The simplified explanation: if the atmosphere above us was perfectly transparent (so that the sun's light shined straight through it), the sky would be pitch black. But a phenomenon called “Rayleigh scattering” causes a little of the sun's light to be scattered in random directions, which is why the sky isn't pitch black. Rayleigh scattering is sensitive to the light's wavelengths – shorter wavelengths (the blue end of the spectrum) are scattered more than longer wavelengths.

And that, my friends, is why the sky is blue and not black. Much more, including the interesting effects of Mies scattering, here, here, here, and here.

Mercury

This morning the planet Mercury was at its greatest elongation (angular distance from the sun) as seen from Earth – which means this morning was a great time to try to observe Mercury. No binoculars or telescopes are required; it's plenty bright enough to see with the naked eye. It's been many years since I tried to locate Mercury in the sky, and I remember it being very difficult to find.

Not this time! I went outside at 4:30 am, about 75 minutes before sunrise, and looked over in the direction where the sun would be coming up – and there it was! A small, bright, orangish “star” right where it should be.

The image above is shamelessly stolen from Bryan Brandenburg's excellent blog. More information on the planet Mercury (and viewing it) can be found here, here, here, and here.

Random Numbers

Here's a fact that surprises many people – even many computer professionals: one of the most difficult challenges for a computer system is coming up with a truly random number. In fact, without special “non-deterministic” hardware, it is provably impossible for a computer to generate a truly random number.

The reason for random numbers being a challenge for computers is that computers are, by their very nature, “deterministic”. Everything they do is completely predictable, if you know the software that's running on them. Over the years, many talented computer scientists have invested large efforts in developing so-called “pseudo-random” algorithms. These algorithms generate numbers that appear to be random (in that a human can't predict what the next pseudo-random number will be), but actually are completely predictable and even repeatable. More recently there has been a determined effort (especially with Linux) to build systems that collect some truly random information available to a computer (such as the interval between keystrokes, or the delay between sending a packet and receiving a response, or the time it takes to read data from a hard disk) – but these efforts suffer from the low rate of truly random information and unexpected (non-random) patterns that show up. Truly random numbers – meaning numbers that are provably unpredictable no matter what information you have – are still only possible with special hardware attached to your computer. Such hardware exploits some known-to-be-truly-random (e.g., non-deterministic) natural phenomenon, such as the timing of radioactive decay.

This fact has some important consequences. Probably the two biggest consequences: it means that many cryptographic systems have an inherent weakness, and it means that many computer models (in particular, a common kind of model called the “Monte Carlo model”) exhibit some very undesirable biases.

The weakened cryptographic systems are those that depend on a randomly-selected key. A good example of such a system is the very widely used SSL system – this is what you use every time you go to a secure web site. There's no need to panic about this – it's still true that the effort required to break SSL is far more costly than any benefit an attacker might get – and it's also true (so far) that breaking SSL on the basis of the random key selection is theoretical.

Bias in Monte Carlo models is a problem with more immediate consequences. Such models are the basis of pricing many financial instruments (options, many bonds, and especially complex derivatives); errors of any kind in these models could have millions or even billions of dollars in jeopardy. Another common use of these models is in weather forecasting, where errors could cost millions in unnecessary watering or other agricultural activities. Monte Carlo models are used to test designs for new buildings, bridges, airplanes, etc. – where human safety is at issue. For all of these uses, and the many more uses of Monte Carlo models, truly random numbers are, well, truly needed.

Lists of random numbers have been available on the Internet for quite a while. These are useful, but for large scale and oft-repeated modeling they are not enough. What's been missing – until now – is an Internet-based service for retrieving truly random numbers. Such a service is now available, at the Quantum Random Bit Generator Service. Anyone involved with Monte Carlo models will find this very interesting indeed – and I would expect to see some cryptographic systems make use of this service once the secure version of it becomes available…

The Real War

Strategy Page has an excellent article about the pervasive corruption in Middle Eastern governments, and the challenges of cleaning it up. A sample:

But the war is still not the major problem. Corruption and incompetent government are.

Corruption is pervasive throughout the Middle East, and so common that it is simply accepted by most locals and foreign visitors. But the inability to create a civil society leads to widespread incompetence in government. This is made worse in Iraq, because the 2003 invasion put the ruling class, largely composed of Sunni Arabs, out of power. The Kurds had been free for over a decade, protected by British and American air power. The Kurds still had corruption and a shortage of skills, but they had been able to develop a peacefulness and prosperity that was in sharp contrast to the rest of Iraq. It's amazing what peace and some honest government will do. Northern Iraq is a striking example of what the rest of Iraq could be like. But you can't do it in a hurry.

The article is fairly long, and full of interesting detail and observation:

More American troops are now embedded with Iraqi police and military units. Partly they are there to advise, but mostly they are there to spy. When incompetent or corrupt officials are spotted, the American troops can either turn them around or turn them in.

Go read the whole thing.

Unintended Consequences...

Last fall, California's voters – by a 70% majority – passed “Jessica's Law”. This law makes it illegal for sex offenders to live within 2,000 feet of a school or park. The basic idea is very simple and hard to argue with: keep the sick creeps away from the kids.

Previously a court ruled that the law could only be applied to offenders released after the ballot measure was passed last November. A review of the records of these recently-released offenders shows that about 2,100 of them are living in areas that violate the law. California's cities and towns tend to have large numbers of parks and schools that are widely distributed, and in many communities Jessica's law effectively bars these sex offenders from living in the community at all, as there is no place more than 2,000 feet from a school or park.

And this leads to the unintended consequence: for lack of any other legal place to live, these sex offenders will be forced to move to rural areas. When you consider the large number of these sex offenders (and that's depressing enough all by itself!), it becomes obvious that having them all moving into the rural areas is a real issue – those areas will quickly have a very high proportion of sex offenders in the population. This is a special concern because sex offenders are particularly likely to repeat their offenses; rehabilitated sex offenders are rare stories.

We live in just such a rural area; there is no park or school within 2,000 feet of us. While we don't have any children, we don't much like the idea of these sex offenders – with their known propensity to re-offend – living in our neighborhood. We also don't much like the idea of them living near kids in the city.

I think the real problem is that we let these people roam amongst the public at all. In my opinion, we are far too willing, as a society, to risk our children's safety in order to allow a sex offender to go free. I would much rather see us treat child molesters as seriously ill mental health patients, and incarcerate them in appropriate facilities until and if we can be certain they are “cured” – even if that means they are incarcerated for life.

Cruelty in Santa Rosa

This morning's news includes a hard-to-believe story of animal cruelty: two 15 year old girls setting a trapped 8 week old kitten on fire, and laughing as it burned.

This actually happened last month, in Santa Rosa, California. The news this morning is that the kitten (named “Adam” by the people caring for it) is clinging to life – and the girls have been charged with animal cruelty.

These two girls are obviously not of the “sugar, spice, and everything nice” variety. I rather miss those old-fashioned sorts of young girls…

Color Perception

The way we perceive color is very different from what you might think (if you've ever thought about this at all!). When someone with normal color vision looks around them, they see a world full of colors – an infinite variety of hues and brightnesses. This perception is created by a relatively simple set of color sensors (in the retina at the back of your eyeball) and a lot of fancy interpretation by your brain.

Consider this simple-sounding color perception example – the color of a tiny patch of clear blue sky. You perceive that as a specific color: a bright, light blue. In actual fact, the “color” of the sky is much more complex than that. It is not a high intensity of a single wavelength of visible light (as a laser is); instead, it is a mix of a broad range of wavelengths from very short ultraviolet light to very long infrared light. The blue end of these wavelengths are slightly higher intensity than the red end, and we perceive the mix as the bright, light blue of the sky.

The physical mechanism by which our eyes sense the various wavelengths of light is well understood. Our retinas have “sensors” (the so-called “cones”) that respond to three different sections of the visible light spectrum. The graph at right shows their response in a typical person – as you can see, it is quite arbitrary. In the case of our hypothetical blue sky, all three sensors would respond: the S cones (blue) most intensely, the M cones (green) slightly less intensely, and the L cones (red) even slightly less. Our brain takes that combination and interprets it as the bright, light blue of the sky.

A digital camera has sensors that mimic those of our eyes; the better cameras do so quite closely. A camera taking a photo of our example's patch of sky would record the color as intensities of red, green, and blue: something like 100% blue, 99.6% green, and 99.4% red. If you were to view that photo on your computer monitor, three different tiny dots – one red, one green, one blue (look at your screen with a magnifying glass and you can see them!) – each lit up brightly, with the blue one slightly brighter. Our eyes see that mix of three wavelengths as being nearly identical to the broad range of wavelengths in the real blue sky, and we're successfully tricked into seeing the same color.

A different kind of camera sensor is under development today – one that can record the actual spectrum at every tiny piece (“pixel”) of a photo. For scientific purposes, this is incredibly valuable information. Often it is possible to identify a particular substance (such as a particular metal, mineral, etc.) from the reflected spectrum of light. Such a camera mounted on a robot space explorer could identify all the minerals it could see on the surface of a planet; on a military vehicle, it could see the difference between natural objects and camouflaged objects. One could imagine all kinds of interesting things to do with images that have so much information in them. For example, software might analyze such images to locate wildlife – so someone might build a pair of binoculars that automatically pointed out the wildlife to you!

Currently there is no system that I'm aware of that can reproduce such an image with a full spectrum of wavelengths – but if we were to imagine such a system, then the spectrum imaging camera's photos could be seen in exactly the same way as they originally appeared. Such an image would be indistinguishable from the real thing, even by sensitive scientific instruments.

The next few years of imaging technology promise to be very interesting indeed. Many companies and scientists are working on this technology, some aimed at consumer cameras and others aimed at more exotic objectives – but anything useful is almost certain to end up in readily purchasable cameras, as this area is intensely competitive…

I want those binoculars!

Before and After

This evening I sat down to start restoring a fine old Dring & Fage slide rule, and I finally remembered to do something I've been meaning to do for a long time: show a “before” and “after” photo.

This particular slide rule dates back to the mid-1800s. It's an unusual style, with two slides on each side of the body. The condition of this example is superb, with almost no damage or even signs of wear. The only notable problems are (1) it is filthy, as you might expect from something 150 years old, and (2) the parts fit too tightly to move smoothly.

In the photo above, the top piece is a segment of an uncleaned slide and the bottom piece is a segment of a cleaned slide. This rule has four slides plus a rather large body – it took me 45 minutes to clean the first slide, so the whole rule will probably take about 5 hours to clean.

The cleaning process is simple, but tedious: I soak an old washrag, fold it into quarters on my worktable, sprinkle some Bon Ami onto a corner of the washrag, and then carefully scrub one little piece of my work at a time. The trick is to scrub hard enough to get off all the soiling, but not hard enough to do any damage to the finish – the only way I know how to do this is trial-and-error, starting with very little pressure and working my way up.

Once I've thoroughly scrubbed the entire workpiece, I inspect it carefully for any firmly adhered stuff. These chunks I carefully work off with dental picks. This particular piece had a few specks of something that looked like wax, plus a few paint droplets. Most of the pieces this old that I restore have far more adhered junk.

The last cleaning step is to rinse the workpiece, which is more of a challenge than it sounds. Slide rules like this have very finely engraved lines on them, and if they're made from certain woods (such as mahogany) open pores. These engravings and pores accumulate soap, feldspar powder from the Bon Ami, and fine particles of whatever the slide rule was exposed to in its life. All of this stuff must be rinsed out, and usually the force of the tap water is not enough – I also have to scrub out all the pores with a very fine, stiff-bristled brush. That last bit can be quite tedious!

Once I've cleaned the entire slide rule, and all the parts are thoroughly dried, I'll apply several coats of Johnson's Paste Wax. That will protect any bare wood that's been exposed, and it will fill in small pores and scratches. I let the wax dry for a few hours and then polish it up with a shoe-polishing rag. In the photo above, the bottom slide has been cleaned but not waxed; it will be a little darker and much shinier once it's been waxed.

One interesting thing I've learned about these old wooden slide rules is that they are impervious to water. When I first started restoring these instruments, I was afraid to get them even slightly wet – I figured that would raise the grain and ruin the finish. After a few accidental soakings caused no harm, I started getting bolder about the use of water – and now I don't hesitate to put a 200 year old instrument directly in the tap water. The only slide rule I've ever damaged with water was an unfinished wooden rule made by Lawrence (an American manufacturer of crude, low-end slide rules), and even that one was easily fixed with a little fine sandpaper. The combination of water and Bon Ami cleans the old wooden instruments better than anything else I've ever found…

Fowler's Universal Calculator

This is a fine example of a watch-style circular slide rule, albeit a very large one – it is 87mm (about 3½ inches) in diameter. Click on the photo at right for a large version, or visit my slide rule collection for all the details.

Using one of these slide rules is a bit more work than an ordinary linear slide rule (turning the knobs is slightly tedious), but they pack a lot of accuracy into a very small package. With its three-segment D scale, this one can multiply and divide with the same accuracy as a linear slide rule that is 49 cm (over 19 inches) long – not back for something that fits conveniently into your pocket!

The Fowler watch-style slide rules (they made many models) seem somehow quintessentially English to me: heavy, sturdy, practical, and yet quite sophisticated. I know of no American-made slide rule even remotely like this one, though several American manufacturers made circular slide rules. There were several English manufacturers of fine watch-style circular slide rules, at least one French manufacturer, and even the Soviets made a cheap imitation. But the English models have a unique style that, for whatever reason, was never duplicated outside of England…

Hit And Run Wreck

Via NBC San Diego, this news (more photos here) of a hit-and-run wreck that seriously injured a mother of four, but spared her kids:

Police said that the driver of a pickup truck took off running after he hit a truck with a mother and her four children inside.

The wreck took place on Monday afternoon on Melody Road in Jamul.

According to investigators, the truck with the family inside was following behind the suspect's pickup, which had pulled over to the shoulder. When the family drove by the truck, its driver pulled out to make a U-turn and slammed into her truck. Authorities said the driver fled the scene. A passenger riding inside the vehicle stayed with the pickup, investigators said. The children were apparently unharmed in the wreck, but their mother was seriously injured.

The driver fled the scene on foot. Given that the police have his truck and his passenger, one would think the police would be able to identify, locate and apprehend him quickly. I sure hope so...

I don't know anything further about this incident. If any of my readers know more, please leave comments with the additional information.

Would You Be Useful?

Imagine you could travel back in time … say, a couple thousand years. Would you be able to teach people about technologies that are now common, but were unknown then? That's the question The Universe As asks:

If you were to travel 2000 years into the past, how useful would you be in jumpstarting technological advancements? This 10 question quiz will help you figure out your technological usefulness. If you do poorly on the quiz, as most people likely will, then just let that inspire you to study up more on how things work and where raw materials come from.

Take the quiz, and leave your score in the comments. I scored 8 out of 10.

Keuffel & Esser 1744

This slide rule (click to enlarge the photo at right) was made around 1897 and sold by Keuffel & Esser. It may have been actually manufactured by Dennert & Pape (in Germany); they made the earlier versions of this model and I'm not sure when Keuffel & Esser actually took over the manufacturing themselves. I've posted this up on my collection web site, including high resolution scans and lots of details.

This one posed an interesting restoration challenge that I had not run into previously – sometime in its history, someone spilled a liquid onto one side of it, and then let the liquid evaporate without cleaning it up. This left a layer of gunk on the slide rule that looked a lot like rust, and was quite difficult to remove – no solvent I have would dent it; I had to soak and abrade it (using Bon Ami). Some staining still remains; I could see under a microscope that the colorant has migrated into the plastic.

In addition, this slide rule had 110 years worth of the grey “gunk” that seems to accumulate on anything that humans touch. I probably really don't want to know what's in it! Usually this gunk cleans off easily with soap or alcohol, but on this slide rule some of the gunk had hardened into something resembling granite. To clean the slide's tongues and grooves I had to resort to carefully picking off the rocky gunk with a dental pick – hard work for these old eyes...

Photo of the Day

I thought you loved me!

Evaporative Cooling

Each summer we depend on our air conditioner to keep our home's temperature at a livable level – otherwise it would be 100°+ in the house, and darned uncomfortable. We have a completely conventional air conditioner (for the U.S.): a standard electric unit that depends on the evaporation and condensation of a synthetic refrigerant. It works great, and keeps our house at a very comfortable temperature – but it costs a small fortune to run. Surely there must be a better way!

And there is.

In any dry part of the country (and we certainly qualify for that!), evaporative cooling is a technology that costs much less for any given cooling capacity. This technology (which comes in several forms) leverages a simple fact about water: it absorbs a lot of heat (2272 Joules) for each gram of water evaporated. Our air conditioner is a “five ton” unit (60,000 BTU/hour). To provide an equivalent amount of cooling, we'd need to evaporate water at the rate of about 7.4 gallons per hour.

Two forms of evaporative cooling are common in homes in certain areas of the U.S.: misting systems and “swamp coolers”. Misting systems force water at high pressure through tiny holes, creating extremely fine droplets that evaporate almost immediately, cooling down the air around them. Many people in Arizona, New Mexico, and other places use misting systems to cool their patios. There are a few of these in the San Diego area, but they are not common. Swamp coolers work by blowing air through a porous pad that is kept wet, usually by rolling the pad continuously through a tub of water. The air is then routed into the home, directly cooling the house. These systems are common in some areas (again, in Arizona and New Mexico), but they have one big drawback: they raise the humidity in the house to undesirably high levels.

The third form of evaporative cooling technology isn't found (to my knowledge) in homes at all, though it is quite common in industrial buildings. This is the “forced-draft cooling tower”, which works by forcing air over droplets of water to cool the water. A conventional heat exchanger then runs a separate loop (of refrigerant or chilled water) to heat exchangers in the building being cooled. These cooling tower system are slightly less efficient than swamp coolers (as there are some thermal losses in the heat exchanger loop), but they have the great advantage of not humidifying the air in the building being cooled. The only reason I can think of that these are not used for homes is that they are relatively complex pieces of machinery. A small capacity cooling tower is just as complex as a large one, and would probably be much more expensive to build than a small capacity refrigerant-based air conditioner. But much cheaper to run!

To cool our home on a typical summer day, I estimate that we'd have to evaporate about 40 gallons of water. I'm exploring the notion of building my own cooling tower to replace our conventional system. The basic engineering challenge is to create enough droplets, with air blowing over them, to evaporate water at the required rate of 7.4 gallons/hour; I've not yet found any reference that would help me design this. The rest of it is very straightforward, basically just plumbing.

Any “evaporation engineers” out there?

Orbital Mechanics

Maneuvering a spacecraft in orbit requires some tactics that most of us would find counter-intuitive. This morning I got to pondering exactly how a simple maneuver would be accomplished. I set my self a simple problem: suppose I was in a perfectly circular orbit, 1 kilometer (0.6 miles) further from Earth than the space station I wanted to dock with, which was orbiting in a perfectly circular orbit at 500 kilometers (311 miles) above the Earth's surface. What maneuvers would I need to make?

Orbital mechanics doesn't get much simpler than this.

First thing you'd notice is that the space station is moving ahead of you in its orbit. That's because at its slightly lower altitude, it needs to move about a half millimeter per second (1.2 miles per hour) faster than you in order to stay in orbit. That's a leisurely walking pace, so you'd see the space station moving slowly past you – and you'd be forgiven for thinking that you had to speed up to “catch up” to it. But in fact, you need to do exactly the opposite! You need to slow down very slightly so that you will fall down to its altitude. So you aim your maneuvering rocket to slow yourself down, and light it off for a short blast, just enough to put you into an elliptical orbit whose perigee (low point) is 500 kilometers.

Now you're moving more slowly, and falling behind the space station more quickly – but as you fall, you gain a little more speed (just as you would if you jumped off a stool). Not enough to catch up, though, and when you've fallen to 500 kilometers, you're still a little bit behind the space station. But no matter – because you're in an elliptical orbit, you're actually traveling ever-so-slightly faster than the space station, so you slowly approach it. At that point, you need to slow down some more, to match the space station's speed and orbit.

You started out above the space station, moving more slowly than it was. You made two maneuvers to dock with it: both of them slowing you down! It seems weird, and somehow wrong, but that's really how it works. All of the strangeness derives from a simple fact: satellites in higher orbits have more energy than those in lower orbits. We had to slow down (twice!) to dock with the space station because we were in a higher orbit, and had more energy (for our mass) than the space station did – so we had to get rid of some...

The above analysis is based on a simple formula for the velocity of a satellite in a perfectly circular orbit around the Earth. The formula, along with other information, can be found here, here, and here.